Field of the Invention
The present invention relates to a wireless communication system, and more particularly to a method for generating a codebook in a multiple input multiple output (MIMO) wireless communication system.
Discussion of the Related Art
The present invention relates to the STBC-SSC (space time block code-spatial sequence coding) scheme for use in the open loop MIMO (multiple input multiple output) system. When RF data is transmitted and received using the Alamouti STBC scheme, a user equipment (UE) may apply a conjugate complex number to the data symbol received at an even time point (or at an odd time point), and may store the resultant value therein. The above operation is a UE operation corresponding to the Alamouti codeword by which the row/column vectors of the effective channel matrix are perpendicular to each other. When considering the UE operation, the number of antenna index sequences (hereinafter referred to as “sequences”) capable of being constructed by the conventional STBC-SSC scheme is reduced, so that advantages of the STBC-SSC scheme may be deteriorated. In addition, if the number of sequence decoding errors increases even when many sequences can be constructed, the number of Tx symbol errors may also increase, such that it may be difficult to actually utilize many sequences.
In order to address the above-mentioned issue, the present invention provides a method for generating the sequence more effectively than the legacy STBC-SSC scheme in consideration of the above UE operation. In addition, the present invention provides a method for designing a sequence codebook to reduce the probability of error generation between the sequences in such a manner that data can be loaded on the resultant sequence.
Prior to describing the present invention, the SM scheme and the STBC-SM scheme will hereinafter be described in detail.
In addition, the present invention modifies a codeword matrix for use in GBD-QOSTBC (Generalized block diagonal quasi-orthogonal space time block code) so that it defines a sequence (composed of an antenna index) capable of being identified by a user equipment (UE) in different ways. GBD-QOSTBC will hereinafter be described in detail.
Assuming that the number of Tx antennas is denoted by MT, the (MT×MT)-sized GBD-QOSTBC codeword matrix is constructed. The Alamouti codeword corresponding to MT=2 is defined as the matrix A(si,sj) as shown in the following Table 1. The symbols si,sj may be complex symbols (i.e., si,sjεΨ) over signal constellation (Ψ).
                                          A            ⁡                          (                                                s                  i                                ,                                  s                  j                                            )                                =                      [                                                                                s                    i                                                                                        s                    j                                                                                                                    -                                          s                      j                      *                                                                                                            s                    i                    *                                                                        ]                          ⁢                                  ⁢                  (                      where            ,                          i              ∈                              {                                  1                  ,                  3                  ,                                                            …                      ⁢                                                                                          ⁢                      2                      ⁢                      k                                        -                    1                                                  }                                      ,                                                  ⁢                          j              ∈                              {                                  2                  ,                  4                  ,                                      …                    ⁢                                                                                  ⁢                    2                    ⁢                    k                                                  }                                      ,                          k              =                                                M                  T                                /                2                                              )                                    [                  Equation          ⁢                                          ⁢          1                ]            
In the environment (MT=4) based on Equation 1, the QO-STBC code is represented by the ABBA code as shown in the following equation 2.
                              [                                                    A                                            B                                                                    B                                            A                                              ]                =                  [                                                                      s                  1                                                                              s                  2                                                                              s                  3                                                                              s                  4                                                                                                      -                                      s                    2                    *                                                                                                s                  1                  *                                                                              -                                      s                    4                    *                                                                                                s                  3                  *                                                                                                      s                  3                                                                              s                  4                                                                              s                  1                                                                              s                  2                                                                                                      -                                      s                    4                    *                                                                                                s                  3                  *                                                                              -                                      s                    2                    *                                                                                                s                  1                  *                                                              ]                                    [                  Equation          ⁢                                          ⁢          2                ]            
In Equation 2, a diversity gain capable of being obtained using the ABBA code is still maintained at the value of 2. Therefore, a phase rotation of the (s3,s4) symbol is needed to obtain the diversity gain of 4 corresponding to the number of Tx antennas. The phase-rotated QO-STBC codeword matrix may be defined as shown in the following equation 3.
                              C          4                =                              [                                                                                s                    1                                                                                        s                    2                                                                                                              s                      ~                                        3                                                                                                              s                      ~                                        4                                                                                                                    -                                          s                      2                      *                                                                                                            s                    1                    *                                                                                        -                                                                  s                        ~                                            4                      *                                                                                                                                  s                      ~                                        3                    *                                                                                                                                          s                      ~                                        3                                                                                                              s                      ~                                        4                                                                                        s                    1                                                                                        s                    2                                                                                                                    -                                                                  s                        ~                                            4                      *                                                                                                                                  s                      ~                                        3                    *                                                                                        -                                          s                      2                      *                                                                                                            s                    1                    *                                                                        ]                    =                      [                                                                                A                    ⁡                                          (                                                                        s                          1                                                ,                                                  s                          2                                                                    )                                                                                                            A                    ⁡                                          (                                                                                                    s                            ~                                                    3                                                ,                                                                              s                            ~                                                    4                                                                    )                                                                                                                                        A                    ⁡                                          (                                                                                                    s                            ~                                                    3                                                ,                                                                              s                            ~                                                    4                                                                    )                                                                                                            A                    ⁡                                          (                                                                        s                          1                                                ,                                                  s                          2                                                                    )                                                                                            ]                                              [                  Equation          ⁢                                          ⁢          3                ]            
In Equations 2 and 3, s1,s2,s3,s4εΨ may be used, and {tilde over (s)}3,{tilde over (s)}4εejθ1Ψ (where, {tilde over (s)}3=s3·ejθ1,{tilde over (s)}4=s4·ejθ1) may be used. Specifically, in order to modify the Q-OSTBC matrix shown in Equation 3 into a block diagonal matrix (GBD-QOSTBC), a symbol corresponding to an odd index and a symbol corresponding to an even index are defined in different ways in association with the symbols (s1,s2εΨ,{tilde over (s)}3,{tilde over (s)}4εejθ1Ψ) located over the signal constellation. That is, the odd index symbol may be defined as sodd=[s1 s3 . . . s2k−1]T, and the even index symbol may be defined as seven=[s2 s4 . . . s2k]T.
The following linear operation is applied to the above symbols, so that new symbols may be defined as shown in Equation 4.[S1S3 . . . S2k−1]T=TDsodd [S2S4 . . . S2k]T=TDseven  [Equation 4]
In order to discriminate the signal constellation of the newly defined symbols shown in Equation 4, Γ may be defined. In other words, the symbol of Equation 4 may be defined as SjεΓ.
In Equation 4, 2k symbols may be classified into two sets (or two aggregates) according to the odd and even indexes. In this case, the (k×k) matrix T may be a random Hadamard matrix. A phase rotation matrix D for acquiring a maximum diversity gain may be represented by the following equation 5.
                    D        =                  [                                                                      ⅇ                                      jθ                    0                                                                                                                                                                                                                                                                                                                                                                                                                                                ⅇ                                      jθ                    1                                                                                                                                                                                                                                                                                                                                                                                                                              ⋱                                                                                                                                                                                                                                                                                                                                                                                                              ⅇ                                      jθ                                          k                      -                      1                                                                                                    ]                                    [                  Equation          ⁢                                          ⁢          5                ]            
Assuming that the Hadamard matrix
  T  =      [                            1                          1                                      1                                      -            1                                ]  shown in Equation 4 is used, the equation 3 may be re-defined as a block diagonal matrix as shown in the following equation 6.
                                          C            ^                    4                =                              [                                                                                A                    ⁡                                          (                                                                                                    s                            1                                                    +                                                                                    s                              ~                                                        3                                                                          ,                                                                              s                            2                                                    +                                                                                    s                              ~                                                        4                                                                                              )                                                                                        0                                                                              0                                                                      A                    ⁡                                          (                                                                                                    s                            1                                                    -                                                                                    s                              ~                                                        3                                                                          ,                                                                              s                            2                                                    -                                                                                    s                              ~                                                        4                                                                                              )                                                                                            ]                    =                                                 [                                                                                                                                                                        S                            1                                                                                                                                S                            2                                                                                                                                                                            -                                                          S                              2                              *                                                                                                                                                            S                            1                            *                                                                                                                                                    0                                                                                        0                                                                                                                                                            S                            3                                                                                                                                S                            4                                                                                                                                                                            -                                                          S                              4                              *                                                                                                                                                            S                            3                            *                                                                                                                                                          ]                                                          [                  Equation          ⁢                                          ⁢          6                ]            
In Equations 4 and 6, the symbols (s1,s2) may be symbols located over the original signal constellation Ψ in which no phase rotation occurs, such that θ0=0 of the matrix D may be decided. In addition, although the conventional QO-STBC codeword matrix (C4) shown in Equation 3 is different from the GBD-QOSTBC codeword matrix (Ĉ4) shown in Equation 6, the conventional QO-STBC codeword matrix (C4) and the GBD-QOSTBC codeword matrix (Ĉ4) may have the same average BER performance.
In another example of GBD-QOSTBC, the codeword matrix (C8) corresponding to MT=8 may be used. In association with a total of 8 Tx symbols, two symbols are combined into one pair, and symbols of different pairs may belong to the signal constellation having rotated in different phases as shown in the following equation 7.s1,s2εejθ0Ψ,{tilde over (s)}3,{tilde over (s)}4εejθ1Ψ,s5,s6εejθ2Ψ,ŝ7,ŝ8εejθ3Ψ  [Equation 7]
In Equation 7, θ0=0 may be decided. The phase may be determined according to the number of antennas and the modulation order of Tx symbols. Assuming that MT=8 is decided and the BPSK symbol is transmitted,
            θ      1        =          π      4        ,            θ      2        =                  2        ⁢        π            4        ,            θ      3        =                  3        ⁢        π            4      may be used. The random Hadamard matrix (T) shown in FIG. 4 may be assumed as shown in the following equation 8.
                    T        =                  [                                                    1                                                              -                  1                                                            1                                                              -                  1                                                                                    1                                            1                                                              -                  1                                                                              -                  1                                                                                                      -                  1                                                            1                                            1                                                              -                  1                                                                                    1                                            1                                            1                                            1                                              ]                                    [                  Equation          ⁢                                          ⁢          8                ]            
In addition, the codeword matrix (C8) may be represented as shown in the following equation 9.
                              C          8                =                              [                                                  ⁢                                                                                A                    1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A                    2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A                    3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    A                    4                                                                        ]                    =                                                                                   [                                                                          ⁢                                                                                                              S                          1                                                                                                                      S                          2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  -                                                      S                            2                            *                                                                                                                                                S                          1                          *                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              S                          3                                                                                                                      S                          4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ⁢                                                      -                                                          S                              4                              *                                                                                                                                                                            S                          3                          *                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ⁢                                                      S                            5                                                                                                                                                S                          6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ⁢                                                      -                                                          S                              6                              *                                                                                                                                                                            S                          5                          *                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              S                          7                                                                                                                      S                          8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  -                                                      S                            8                            *                                                                                                                                                S                          7                          *                                                                                                      ⁢                                                                          ]                                ⁢                                                                  ⁢                                  A                  1                                            =                                                A                  (                                                                                    s                        1                                            -                                                                        s                          ~                                                3                                            +                                                                        s                          _                                                5                                            -                                                                        s                          ^                                                7                                                              ,                                                                  s                        2                                            -                                                                        s                          ~                                                4                                            +                                                                        s                          _                                                6                                            -                                                                        s                          ^                                                8                                                                              )                                =                                                                            A                      ⁡                                              (                                                                              S                            1                                                    ,                                                      S                            2                                                                          )                                                              ⁢                                                                                  ⁢                                          A                      2                                                        =                                                            A                      (                                                                                                    s                            1                                                    +                                                                                    s                              ~                                                        3                                                    -                                                                                    s                              _                                                        5                                                    -                                                                                    s                              ^                                                        7                                                                          ,                                                                              s                            2                                                    +                                                                                    s                              ~                                                        4                                                    -                                                                                    s                              _                                                        6                                                    -                                                                                    s                              ^                                                        8                                                                                              )                                        =                                                                                            A                          ⁡                                                      (                                                                                          S                                3                                                            ,                                                              S                                4                                                                                      )                                                                          ⁢                                                                                                  ⁢                                                  A                          3                                                                    =                                                                        A                          (                                                                                                                    -                                                                  s                                  1                                                                                            +                                                                                                s                                  ~                                                                3                                                            +                                                                                                s                                  _                                                                5                                                            -                                                                                                s                                  ^                                                                7                                                                                      ,                                                                                          -                                                                  s                                  2                                                                                            +                                                                                                s                                  ~                                                                4                                                            +                                                                                                s                                  _                                                                6                                                            -                                                                                                s                                  ^                                                                8                                                                                                              )                                                =                                                                                                            A                              ⁡                                                              (                                                                                                      S                                    5                                                                    ,                                                                      S                                    6                                                                                                  )                                                                                      ⁢                                                                                                                  ⁢                                                          A                              4                                                                                =                                                                                    A                              (                                                                                                                                    s                                    1                                                                    +                                                                                                            s                                      ~                                                                        3                                                                    +                                                                                                            s                                      _                                                                        5                                                                    +                                                                                                            s                                      ^                                                                        7                                                                                                  ,                                                                                                      s                                    2                                                                    +                                                                                                            s                                      ~                                                                        4                                                                    +                                                                                                            s                                      _                                                                        6                                                                    +                                                                                                            s                                      ^                                                                        8                                                                                                                              )                                                        =                                                          A                              ⁡                                                              (                                                                                                      S                                    7                                                                    ,                                                                      S                                    7                                                                                                  )                                                                                                                                                                                                                                                                [                  Equation          ⁢                                          ⁢          9                ]            
The matrix A(si,sj) is defined in Equation 1. Assuming that MT=2k=2r is decided at a random condition denoted by r≧2, the GBD-QOSTBC matrix may be generalized as shown in the following 10.
                              C                      2            ⁢                                                  ⁢            k                          =                  [                                                                      A                  ⁡                                      (                                                                  S                        1                                            ,                                              S                        2                                                              )                                                                                                                                                                                                                                                                                                                                                                                                                                                A                  ⁡                                      (                                                                  S                        3                                            ,                                              S                        4                                                              )                                                                                                                                                                                                                                                                                                                                                                                                                              ⋱                                                                                                                                                                                                                                                                                                                                                                                                              A                  ⁡                                      (                                                                  S                                                                              2                            ⁢                                                                                                                  ⁢                            k                                                    -                          1                                                                    ,                                              S                                                  2                          ⁢                                                                                                          ⁢                          k                                                                                      )                                                                                ]                                    [                  Equation          ⁢                                          ⁢          10                ]            
In the codeword matrix shown in Equation 10, a horizontal axis may denote an antenna index, and a vertical index may denote a timeslot index. In the case of MT=6 in which the number of Tx antennas is not denoted by MT=2k=2r, the GBD-QOSTBC codeword matrix may be constructed in association with MT=8. Then, if the last two rows and the last two columns are deleted, the codeword for MT=6 may be constructed.
The SM scheme will hereinafter be described in detail.
In accordance with the SM scheme, binary data is allocated to each Tx antenna index, an antenna corresponding to a bit stream to be transmitted is selected, and the data stream can be transmitted. That is, total amount of information to be transmitted may be the sum of the amount of information allocated to the data stream and the amount of information allocated to the antenna index.
FIG. 1 is a conceptual diagram illustrating the SM scheme. Referring to FIG. 1, it can be recognized that total amount of information to be transmitted is identical to the sum of the amount of information owned by the Tx symbol and the amount of information allocated to the antenna index used to transmit the Tx symbol information.
In more detail, assuming that the number of Tx antennas is MT, a maximum of log2 MT bits may be allocated to the Tx antenna index. Assuming that the PSK or QAM symbol having the modulation order of M is used, total amount (m) of information capable of being transmitted using the SM scheme may be defined as m=log2(MT)+log2(M). That is, the total amount (m) of information capable of being represented by bits per channel use may be defined as m=log2(MT)+log2(M).
For example, assuming that 3 bits are transmitted per channel use, when the number of Tx antennas is set to 2 and the modulation order is set to 4, the SM scheme may be used as shown in the following Table 1. In Table 1, MT=Nt is set, the number of antennas is an antenna index, and the Tx symbol is an M-PSK or M-QAM symbol.
TABLE 1Nt = 2, M = 4Nt = 4, M = 2InputAntennaTransmitAntennaTransmitbitsnumbersymbolnumbersymbol0001+1+j1−10011−1+j1+10101−1−j2−10111+1−j2+11002+1+j3−11012−1+j3+11102−1−j4−11112+1−j4+1
The STBC-SM scheme will hereinafter be described in detail.
It is assumed that the (L×L) STBC codeword is based on L Tx antennas from among a total number (MT) of Tx antennas. Whereas the SM scheme allocates the bit stream to each antenna index, L selected antennas must be continuously used during a timeslot of the STBC codeword length (L) when data is transmitted according to the STBC-SM scheme.
The amount of information (represented by the number of bits per channel use) capable of being loaded on the antenna index and then transmitted may be denoted by
      1    L    ⁢            ⌊                        log          2                ⁡                  (                                                                      M                  T                                                                                    L                                              )                    ⌋        .  Therefore, the total amount (m) of information, which is loaded on the Tx symbol (M-PSK or M-QAM) and the antenna index and then transmitted, may be defined as
  m  =                    1        L            ⁢              ⌊                              log            2                    ⁡                      (                                                                                M                    T                                                                                                L                                                      )                          ⌋              +                            log          2                ⁡                  (          M          )                    .      
For convenience of description, it is assumed that MT=4, L=2,
            ⌊                        log          2                ⁡                  (                                                                      M                  T                                                                                    L                                              )                    ⌋        =                  ⌊                              log            2                    ⁢          6                ⌋            =      2        ,and M=2(BPSK) may be used.
2 Tx antennas from among four Tx antennas are selected, and data is transmitted using the Alamouti method during 2 timeslots. 2 Tx antenna indexes are selected from among 4 Tx antenna indexes (1˜4), and 2 bits are allocated as shown in the following Table 2. The STBC-SM codeword corresponding to the selected antenna is shown in the following equation 11. In Equation 11, a vertical axis may denote an antenna index, and a horizontal axis may denote a timeslot index.
TABLE 2Selected antenna Allocated indexesbits(1, 2)00(3, 4)01(2, 3)10(1, 4)11
                              X          1                =                              {                                          X                11                            ,                              X                12                                      }                    =                      {                                          (                                                                                                    x                        1                                                                                                            x                        2                                                                                    0                                                              0                                                                                                                          -                                                  x                          2                          *                                                                                                                                    x                        1                        *                                                                                    0                                                              0                                                                      )                            ,                              (                                                                            0                                                              0                                                                                      x                        1                                                                                                            x                        2                                                                                                                        0                                                              0                                                                                      -                                                  x                          2                          *                                                                                                                                    x                        1                        *                                                                                            )                                      }                                              [                  Equation          ⁢                                          ⁢          11                ]                                          X          2                =                                  ⁢                              {                                          X                21                            ,                              X                22                                      }                    =                                    {                                                (                                                                                    0                                                                                              x                          1                                                                                                                      x                          2                                                                                            0                                                                                                            0                                                                                              -                                                      x                            2                            *                                                                                                                                                x                          1                          *                                                                                            0                                                                              )                                ,                                  (                                                                                                              x                          2                                                                                            0                                                                    0                                                                                              x                          1                                                                                                                                                              x                          1                          *                                                                                            0                                                                    0                                                                                              -                                                      x                            2                            *                                                                                                                                )                                            }                        ⁢                          e                              j                ⁢                                                                  ⁢                θ                                                                                    
In Equation 11, it can be recognized that all codeword elements of the codebook χ2 are phase-rotated by θ, such that the distance between symbols defined in two codebooks is maximized, resulting in improved BER performance. The value (θ) may be changed according to the number of Tx antennas and the modulation order, and it is impossible to search for the value (θ) using the closed Form, such that the value (θ) must be experimentally searched for. A detailed description thereof will hereinafter be described with reference to the attached drawings.
FIG. 2 is a conceptual diagram illustrating the STBC-SM scheme. For convenience of description, it is assumed that θ=π/2 is decided as shown in FIG. 2.
x1,x2 may denote BPSK symbols transmitted from respective antennas. Therefore, during two timeslots, one bit is additionally transmitted to each antenna so that a total of 2 bits may be transmitted to the respective antennas. In addition, 2 bits are additionally transmitted to the antenna index, such that a total of 4 bits can be transmitted. In this case, the 4-bit streams may be denoted by u1,u2,u3,u4 as shown in FIG. 2. Assuming that u1,u2 indicates a bit stream allocated to the antenna index and u3,u4 indicates a bit stream allocated to the BPSK symbol and then transmitted, a block diagram shown in FIG. 2 may be acquired.
In the meantime, under the condition that a channel is unchanged during only the timeslot (L<MT), if it is assumed that L Tx antennas are selected from among MT Tx antennas and data is then transmitted at a fixed transfer rate, the STBC-DM scheme transmits some parts of the total amount of Tx data using the SM scheme. As a result, the amount of information, which is located on the Tx symbol and then transmitted, can be greatly reduced as compared to the method for transmitting data using the conventional (L×L)-sized STBC codeword, resulting in acquisition of a BER gain.
The STBC-SSC codebook will hereinafter be described. In accordance with the STBC-SSC method, the GBD-QOSTBC codeword matrix may be modified under the condition that the QO-STBC diversity gain is maintained, resulting in acquisition of the same effect as in the case in which the antennas (1˜MT) are not sequentially used according to the data Tx time points.
Since various antenna patterns can be used during the data Tx time (MT), the sequence composed of the antenna indexes may be defined to discriminate among different patterns. A binary bit stream is allocated to the defined sequence, and the allocated binary bit stream may be used. In order to explain the inventive scheme proposed by the present invention, the codebook defined in the legacy STBC-SSC will hereinafter be described.
(1) χQAM,QOSTBC: QO-STBC symbol vector codebook (comprised of M-PSK and M-QAM symbols)
The QO-STBC symbol vector codebook is used to construct the (MT×MT) codeword matrix based on the legacy QO-STBC scheme. In accordance with the proposed scheme, the QO-STBC symbol vector codebook may be used for GBD-QOSTBC symbol transformation (or conversion). The QO-STBC codeword may be acquired by extending the 2×2 Alamouti codeword (Orthogonal STBC) to the (MT×MT) matrix based on the ABBA codeword in association with MT=22,23, . . . ,2r. Accordingly, the QO-STBC codeword matrix may have half-orthogonal characteristics. That is, each row vector (or each column vector) constructing the QO-STBC codeword matrix may be perpendicular to MT/2 different row vectors (column vectors). In order to easily the above-mentioned characteristics, C4HC4 may be represented by the following equation 12 using the QO-STBC codeword shown in Equation 3.
                                          C            4            H                    ⁢                      C            4                          =                  [                                                    c                                            0                                            d                                            0                                                                    0                                            c                                            0                                            d                                                                    d                                            0                                            c                                            0                                                                    0                                            d                                            0                                            c                                              ]                                    [                  Equation          ⁢                                          ⁢          12                ]            
In Equation 12,
  c  =                                      s          1                            2        +                                    s          2                            2        +                                                s            ~                    3                            2        +                                                s            ~                    4                            2      and d=s1{tilde over (s)}3*+{tilde over (s)}3s1*−s2{tilde over (s)}4*−{tilde over (s)}4s2* may be used. In addition, it can be recognized that the pair of symbols to be joint-ML decoded is composed of (s1,s3),(s2,s4) as can be seen from Equation 12. If the scope of the present invention is extended for a random value (MT), each of two pairs composed of MT/2 symbols needs to be joint-ML decoded.
In conclusion, the χQAM,QOSTBC codebook may be comprised of the codeword vector, the size of which is MT/2×1. Elements of the vector may be symbols, for example, M-PSK, M-QAM, etc. The elements of the vector are composed of a total of MMT/2 vectors, as represented by the following equation 13.
                                                                                          χ                                      QAM                    ,                    QOSTBC                                                  =                                ⁢                                  {                                                            [                                                                                                                                                                  s                                1                                                            ⁡                                                              [                                1                                ]                                                                                                                                                                                          ⋮                                                                                                                                                                                              s                                                                                                      M                                    T                                                                    /                                  2                                                                                            ⁡                                                              [                                1                                ]                                                                                                                                                        ]                                        ,                                          [                                                                                                                                                                  s                                1                                                            ⁡                                                              [                                2                                ]                                                                                                                                                                                          ⋮                                                                                                                                                                                              s                                                                                                      M                                    T                                                                    /                                  2                                                                                            ⁡                                                              [                                2                                ]                                                                                                                                                        ]                                        ,                    …                    ⁢                                                                                  ,                                                                                                                                          ⁢                                  [                                                                                                                                          s                            1                                                    ⁡                                                      [                                                          M                                                                                                M                                  T                                                                /                                2                                                                                      ]                                                                                                                                                              ⋮                                                                                                                                                                  s                                                                                          M                                T                                                            /                              2                                                                                ⁡                                                      [                                                          M                                                                                                M                                  T                                                                /                                2                                                                                      ]                                                                                                                                ]                                }                                                                                        =                                ⁢                                  {                                                            s                      ⁡                                              [                        1                        ]                                                              ,                                          s                      ⁡                                              [                        2                        ]                                                              ,                    …                    ⁢                                                                                  ,                                          s                      ⁡                                              [                                                  M                                                                                    M                              T                                                        /                            2                                                                          ]                                                                              }                                                                    ⁢                                                      [                  Equation          ⁢                                          ⁢          13                ]            
In Equation 13, sn[k]εΨ may be used, where kε{1,2, . . . MMT/2},nε{1,2, . . . ,M2/2}.
(2) χG-STBC: GBD-QOSTBC symbol vector codebook
By means of the above equation 4, the codeword vectors of χQAM,QOSTBC defined as the QAM or PSK symbol may be converted into the GBD-QOSTBC symbols as shown in the following equation 14.
                                                                                          X                                      G                    -                    STBC                                                  =                                ⁢                                  {                                                            TDs                      ⁡                                              [                        1                        ]                                                              ,                                          TDs                      ⁡                                              [                        2                        ]                                                              ,                    …                    ⁢                                                                                  ,                                          TDs                      ⁡                                              [                                                  M                                                                                    M                              T                                                        /                            2                                                                          ]                                                                              }                                            ,                                                                                        ⁢                                                where                  ⁢                                                                          ⁢                                      s                    ⁡                                          [                      k                      ]                                                                      ∈                                  χ                                      QAM                    ,                    QOSTBC                                                                                                                          =                            ⁢                                                {                                                            S                      ⁡                                              [                        1                        ]                                                              ,                                          S                      ⁡                                              [                        2                        ]                                                              ,                    …                    ⁢                                                                                  ,                                          S                      ⁡                                              [                                                  M                                                                                    M                              T                                                        /                            2                                                                          ]                                                                              }                                =                                                                                                      ⁢                              {                                                      [                                                                                                                                                      S                              1                                                        ⁡                                                          [                              1                              ]                                                                                                                                                                            ⋮                                                                                                                                                                                S                                                                                                M                                  T                                                                /                                2                                                                                      ⁡                                                          [                              1                              ]                                                                                                                                            ]                                    ,                                      [                                                                                                                                                      S                              1                                                        ⁡                                                          [                              2                              ]                                                                                                                                                                            ⋮                                                                                                                                                                                S                                                                                                M                                  T                                                                /                                2                                                                                      ⁡                                                          [                              2                              ]                                                                                                                                            ]                                    ,                  …                  ⁢                                                                          ,                                                                                                                      ⁢                              [                                                                                                                              S                          1                                                ⁡                                                  [                                                      M                                                                                          M                                T                                                            /                              2                                                                                ]                                                                                                                                                ⋮                                                                                                                                                    S                                                                                    M                              T                                                        /                            2                                                                          ⁡                                                  [                                                      M                                                                                          M                                T                                                            /                              2                                                                                ]                                                                                                                    ]                            }                                                          [                  Equation          ⁢                                          ⁢          14                ]            
Equation 14 may be understood as one-to-one mapping (1:1 mapping) between the codeword vectors as shown in the following equation 15.
                                                                        s                ⁡                                  [                  1                  ]                                            →                              S                ⁡                                  [                  1                  ]                                                                                                                        s                ⁡                                  [                  2                  ]                                            →                              S                ⁡                                  [                  2                  ]                                                                                          ⋮                                                                              s                ⁡                                  [                                      M                                                                  M                        T                                            /                      2                                                        ]                                            →                              S                ⁡                                  [                                      M                                                                  M                        T                                            /                      2                                                        ]                                                                                        [                  Equation          ⁢                                          ⁢          15                ]            
Referring to Equations 14 and 15, since mapping is achieved on a vector basis, the codeword vector of χG-STBC located nearest to the Rx signal vector is decided, and the symbol vector composed of the QAM symbol of χQAM,QOSTBC is detected through the inverse operation. Symbols used in Equation 14 are summarized as follows.                S[k]: MT/2×1-sized codeword vector        Sj[k]: elements of the vector S[k], jε{1,2, . . . MT/2}        Sj[k]εΓ        
(3) χAnt: Antenna index sequence codebook
2 consecutive timeslots may be denoted by one unit as represented by t=(1,2),(3,4), . . . ,(MT−1,MT), and an antenna index to be used in response to the transmission (Tx) time may be defined. That is, two antenna indexes to be used in 2 consecutive timeslots may be defined. Two antennas may be combined into one pair so that the two antennas may serve as one symbol constructing the antenna index sequence. Therefore, MT/2 antenna pairs may construct one sequence, and the set of different antenna index sequences is denoted by χAnt. The antenna sequence codebook χAnt may be represented by the following equation 16.χAnt={Ij,uj, where jε{1,2, . . . ,2BSSC}}  [Equation 16]
In Equation 16, BSSC is the amount of information allocated to the antenna index sequence and then transmitted, and is represented on a bit basis. In addition, Ij is the j-th antenna index sequence, and uj is a bit sequence corresponding to Ij. In more detail, Ij and uj may be represented by the following equation 17.Ij=(l1,l2),(l3,l4), . . . ,(lMT−1,lMT), uj=[u1,u2,u3, . . . ,uBSSC]li≠lj,∀i,∀jε{1,2, . . . ,2BSSC},ubε{0,1},bε{1, . . . ,BSSC}ui≠uj,∀i,∀jε{1,2, . . . ,2BSSC}.  [Equation 17]
(4) χH: The set of effective channel matrices
χH is the set of (MT×MT)-sized effective channel matrices corresponding to the antenna index sequence defined in the codebook χAnt. This information is owned by only the open loop MIMO system, and may be represented by the following equation 18.χH={Ĥ1,Ĥ2, . . . ,Ĥ2BSSC},Ĥjε,jε{1,2, . . . ,2BSSC}  [Equation 18]
In Equation 18, BSSC is the amount of information allocated to the antenna index sequence in the same manner as described above. The matrix Ĥj may be decided by Ij of χAnt. Assuming that data is transmitted using the j-th antenna sequence and the pair of Tx antennas used in 2 timeslots (t0,t0+1) is denoted by (m1,m2), four elements of the effective channel Ĥj corresponding to (m1,m2) may be represented by the following expression.
[Expression]Ĥj(m1,t0)=h(m1)Ĥj(m1,t0+1)=h(m2)Ĥj(m2,t0)=−h(m1)*Ĥj(m2,t0+1)=h(m2)*
In the above expression, h=[h1 h2 . . . hMT] may be used, and h(m2) is the m2-th element of the vector (h), where a subscript ‘*’ may denote a conjugate complex number. It is assumed that respective elements may be independently from each other, and may have the same independent and identically distributed Gaussian elements, and different vector channels may be independent of each other.